What you can do with the combings from a sheep’s back is the subject of a fascinating display of jazzy carpets, sofas dressed in pinstriped suiting, chairs covered in recycled Aran cable cardigans — and a replica of the white bespoke trouser suit that Bianca Jagger wore to her 1971 wedding.

Add hats that look like Viking headgear and a stuffed brown bear in a woolly all-in-one suit dubbed “crochet-dermy” and you get the controlled madness of “Wool House.”

Staged in the grand, interconnecting rooms of London’s Somerset House (through March 24), the exhibition of interiors and fashion is part of the Campaign for Wool, set up in 2010 and endorsed by Charles, the Prince of Wales.

The idea behind the campaign is to involve a global community, starting with farmers, to emphasize the benefits of wool to textile manufacturers, carpet makers, interior and fashion designers.

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A nursery by Donna Wilson, complete with a sheep-skin sheep by Hanns-Peter Krafft for Thorsten Van Elten at the Wool House Exhibition.Credit
Eamonn McCormack/Getty Images for Wool House

This is in a climate where man-made materials have gained credibility and market share. High-tech materials such as puffer nylon provide modern substitutes to the world’s oldest way of keeping warm.

In another initiative to encourage wool growers, Ermenegildo Zegna, the Italian luxury men’s wear brand, will celebrate in Australia next month half a century of support of the wool industry.

On April 23, a series of events in Sydney will mark 50 years since the foundation in Tasmania of the Ermenegildo Zegna Wool Awards, which include a Golden Fleece trophy, given to the wool grower with the finest raw fleece.

Over the years, a historic and artistic ceramic plate with a horned ram’s head designed by the British artist Graham Sutherland underscored how far Zegna has moved to award and reward wool growers in Australia, particularly in Tasmania, and New Zealand. Those raw fleeces then pass through the Zegna mill in the mountainous Biella district of Italy.

What does the current exhibition do to put the focus on wool?

Arabella McNie, the curator of the Somerset House exhibition, set out to show “how wool can inhabit a space.” That includes art pieces, such as a wall hanging designed by Alexander McQueen for the Rug Company or exceptional felted tapestry by the Dutch designer Claudy Jongstra. Her textural creations, used as wall hangings, are the nearest the show gets to fine art.

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Shoes made with wool, designed by Vivienne Westwood, on display at the Wool House exhibition.Credit
Natasha Cowan/IHT

Another striking piece is a carpet of colorful squares. Designed by Cristian Zuzunaga of Barcelona, the runner flows down the long corridor connecting half of the 16 display rooms.

“This is the country room, designed by Josephine Ryan, who is all about texture and raw, earthy tones,” said Ms. McNie, referring to the “Irish” room, with its scrubbed wooden table and bench and recycled knit on the chairs.

In vivid contrast, next door is the home of the colorful acoustics from Anne Kyyrö Quinn, who says that she works mainly with architects and interior designers on corporate projects. But her attractive three dimensional feltings would brighten any home — as well as serving as a sound absorber.

The nursery by textile designer Donna Wilson celebrates the tactile, from the woolly toy sheep through a “fantastic fox” to felt wallpaper and a tent blanket thrown over a small wooden frame.

“We wanted a nursery that would feed a child’s imagination,” said Ms. McNie, whose own design contribution is a multiethnic room showing the heritage of wool by re-creating in contemporary shapes Turkish saddle bags and cushion fabrics from fragments of Kelims originally used on yurts.

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A modern room by Anne Kyyrö Quinn with a sound-absorbing wool-felt wall at the Wool House exhibition.Credit
Eamonn McCormack/Getty Images for Wool House

The exhibition is divided between inspiration — as in stately rooms “dressed” in wool by leading interior designers — and craft. Workrooms, with their shelves of multicolored woolen threads, will be active with crafts demonstration and participation.

Does it all add up to a paean for wool and an incentive to weave its threads into every aspect of modern life?

As ever, with a single fabric promotion, there is wonder and excitement at what can be created from a single sheep — but not much encouragement to weave wool in with other fabrics. The small fashion section could do with some more thoughtful experiments between man-made and natural materials.

The few intriguing examples of dragging classic wool into the 21st century is the Dashing Tweed company’s way of bringing optic fibers to the base material (twinkling lights on a suit could be useful for the executive cyclist) and the imaginative inventions of Christopher Raeburn.

The exhibition shows the Raeburn recycling of a traditional guardsman’s felt into a bomber jacket and an Italian treatment of wool that makes water roll off the surface as if it were Teflon.

Such modern inventions may not be as tactile and appealing as a creamy bed made entirely from wool (and supposedly good for the heart rate). But fleece has to be looked at as both a basic and classic material — and as something that can be integrated with the inventive fabrics of today.